A correspondence between modified gravity and General Relativity with scalar fields

TL;DR

This paper introduces a method to translate the complex field equations of nonlinear Ricci-based gravity theories coupled with scalar fields into the more familiar form of Einstein's equations with different scalar fields, facilitating solution finding.

Contribution

It presents a novel procedure to map nonlinear Ricci-based gravity theories with scalar matter into Einstein gravity with transformed scalar fields, enabling new solution generation.

Findings

The method applies to theories with multiple scalar fields.

Explicit examples include $f(R)$ and Eddington-inspired Born-Infeld gravity.

The procedure simplifies analyzing complex gravity models.

Abstract

We describe a novel procedure to map the field equations of nonlinear Ricci-based metric-affine theories of gravity, coupled to scalar matter described by a given Lagrangian, into the field equations of General Relativity coupled to a different scalar field Lagrangian. Our analysis considers examples with a single and $N$ real scalar fields, described either by canonical Lagrangians or by generalized functions of the kinetic and potential terms. In particular, we consider several explicit examples involving $f(R)$ theories and the Eddington-inspired Born-Infeld gravity model, coupled to different scalar field Lagrangians. We show how the nonlinearities of the gravitational sector of these theories can be traded to nonlinearities in the matter fields, and how the procedure allows to find new solutions on both sides of the correspondence. The potential of this procedure for applications of scalar field models in astrophysical and cosmological scenarios is highlighted.